Extended Data Fig. 6. Terahertz time-domain ellipsometry (THz-TDE) on the MiGs-incorporated p-type GaN.

a, Schematic illustrations of three samples, each with a 400 nm-thick p-type GaN epilayer, are shown. These form two control groups: one varying in-situ Mg doping concentration (Sample 1 vs. 3) and the other comparing samples with and without MiGs nanostructures (Sample 1 vs. 2). b, Schematic illustration of the samples featuring a three-layer structure: p-type GaN/n-type GaN/sapphire, irradiated by incoming terahertz electromagnetic waves. Each layer is denoted as 1, 2, and 3, respectively. The thickness parameters, d₁ and d₂, are 400 nm and 3.9 µm, respectively. The optical constants, ${\tilde{\epsilon }}_2$ and ${\tilde{\epsilon }}_3$, were obtained from separate measurements, elaborated in the Methods section. The optical model approximates the p-type GaN layer with MiGs nanostructure on top as a single layer, with the acquired optical constants for ${\tilde{\epsilon }}_1$ of Sample 2 assumed to be an average response of layer 1. c, Ellipsometric parameters (tan Ψ, Δ) measured by THz-TDE. The shading corresponds to the uncertainty in the measured values. The uncertainty region is not visible as it is significantly smaller than the measured values, with a standard deviation of less than 0.003 for the ellipsometric parameters. d, Real (ε′) and imaginary (ε″) parts of the relative permittivity obtained for the p-GaN layers, denoted as ${\tilde{\epsilon }}_1$, are complex relative permittivity of the top, represented as ${\epsilon }^{\prime }-i{\epsilon }^{″}$. The increase in ε″ at lower frequencies is attributed to THz absorption by free carriers. A higher ε″ indicates greater absorption and, consequently, higher conductivity. e, Real (solid circles) σ′ and imaginary (hollow circles) σ″ parts of the conductivity $\tilde{\sigma }$, derived from the relative permittivity spectra of the p-GaN layers, are represented as $\tilde{\sigma }={\sigma }^{\prime }-i{\sigma }^{″}=-i\omega {\epsilon }_0\left({\epsilon }_{s,\mathrm{GaN}}-\tilde{\epsilon }\right)$. The fitting range is set within 1.0−2.5 THz to exclude noise at higher frequencies, which is not shown. The best fit results from a global analysis of the real and imaginary components. By fitting the conductivity spectra to the Drude model, the DC conductivity σ_DC (translated to static resistivity ρ_DC), the scattering time τ, and the damping frequency γ can be estimated by $\tilde{\sigma }={\sigma }_{\mathrm{DC}}/\left(1+i\omega \tau \right)$, as summarized in i. f, Ellipsometric parameters (tan Ψ, Δ) measured from the sapphire substrate and the n-type GaN/sapphire sample. g, Complex refractive index $\tilde{n}=n-i\kappa$ obtained for sapphire and the n-type GaN layer. h, Complex refractive index spectra obtained for the p-type GaN layers and fitted to the Drude model. i, Summary and comparison of the measured transport properties by THz-TDE and Hall-effect van der Pauw methods.

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